Holes

Holes are an interesting case study for ontologists and
epistemologists. Naive, untutored descriptions of the world treat holes
as objects of reference, on a par with ordinary material objects.
(‘There are as many holes in the cheese as there are cookies in
the tin.’) And we often appeal to holes to account for causal
interactions, or to explain the occurrence of certain events.
(‘The water ran out because of the hole in the bucket.’)
Hence there is prima facie evidence for the existence of such
entities. Yet it might be argued that reference to holes is just a
façon de parler, that holes are mere entia
representationis, as-if entities, fictions.

‘A hole?’ the rock chewer grunted.
‘No, not a hole,’ said the will-o'-the-wisp despairingly.
‘A hole, after all, is something. This is nothing at
all’. (Ende 1974/1985: 24)

Hole representations—no matter whether veridical—appear to
be commonplace in human cognition. Not only do people have the
impression of seeing holes; they also form a corresponding concept,
which is normally lexicalised as a noun in ordinary languages. (Some
languages even discriminate different types of hole, distinguishing
e.g. between inner cavities and see-through
perforations.) Moreover, data from developmental psychology
and the psychology of perception confirm that infants and adults are
able to perceive, count, and track holes just as easily as they
perceive, count, and track paradigm material objects such as cookies
and tins (Giralt & Bloom 2000; Nelson & Palmer 2001). These
facts do not prove that holes and material objects are on equal
psychological footing, let alone on equal metaphysical footing. But
they indicate that the concept of a hole is of significant salience in
the common-sense picture of the world, specifically of the
spatiotemporal world.

If holes are entities of a kind, then, they appear to be
spatiotemporal particulars, like cookies and tins and unlike numbers
or moral values. They appear to have a determinate shape, a size, and
a location. (‘These things have birthplaces and histories. They
can change, and things can happen to them’, Hofstadter &
Dennett 1981: 6–7.) On the other hand, if holes are particulars,
then they are not particulars of the familiar sort. For holes appear
to be immaterial: every hole has a material
“host” (the stuff around it, such as the edible part of a
donut) and it may have a material “guest” (such as the
liquid filling a cavity), but it does not itself seem to be made of
matter. Indeed, holes seem to be made of nothing, if anything
is. And this gives rise to a number of conundrums. For example:

It is difficult to explain how holes can in fact be perceived. If
perception is grounded on causation, as Locke urged (Essay,
II-viii-6), and if causality has to do with materiality, then
immaterial bodies cannot be the source of any causal flow. So a causal
theory of perception would not apply to holes. Our impression of
perceiving holes would then be a sort of systematic illusion, on pain
of rejecting causal accounts of perception. (On the other hand, if one
accepts that absences can be causally efficacious, as urged by Lewis
2004, then a causal account could maintain that we truly perceive
holes; see Sorensen 2008.)

It is difficult to specify identity criteria for holes—more
difficult than for ordinary material objects. As holes are immaterial,
we cannot account for the identity of a hole via the identity
of any constituting stuff. But neither can we rely on the identity
conditions of its material host, for we can imagine changing the
host—partly or wholly, gradually or abruptly—without
affecting the hole. And we cannot rely on the identity conditions of
its guest, for it would seem that we can empty a hole of whatever
might partially or fully occupy it and leave the hole intact.

It is equally difficult to account for the mereology of
holes. Take a card and punch a hole in it. You have made one hole. Now
punch again next to it. Have you made another hole? In a way, yes: now
the card is doubly perforated. But what prevents us from saying that
we still have one hole, though a hole that comes in two disconnected
parts? After all, material objects can be disconnected: a bikini, your
copy of the Recherche, a token of the lowercase letter
‘i’. Perhaps holes may be disconnected, too? If so,
perhaps we have just punched a single, disconnected hole?

It is also difficult to assess the explanatory relevance of holes.
Arguably, whenever a physical interaction can be explained by appeal to
the concept of a hole, a matching explanation can be offered invoking
only material objects and their properties. (That water flowed out of
the bucket is explained by a number of facts about water fluidity,
combined with an accurate account of the physical and geometric
conditions of the bucket.) Aren't these latter explanations
enough?

Further problems arise from the ambiguous status of holes in
figure-ground displays (Bozzi 1975). Thus, for example, though it
appears that the shapes of holes can be recognized by humans as
accurately as the shapes of ordinary objects, the area seen through a
hole typically belongs to the background of its host, and there is
evidence to the effect that background regions are not represented as
having shapes (Bertamini & Croucher 2003; Bertamini & Casati
2014). So what would the shape of a hole be, if any?

These difficulties—along with some form of horror
vacui—may lead a philosopher to favor ontological parsimony
or revisionism over naive realism about holes. A number of options are
available:

One may hold that holes do not exist at all, arguing that all
truths about holes boil down to truths about holed objects (Jackson
1977: 132). This calls for a systematic way of paraphrasing every
hole-committing sentence by means of a sentence that does not refer to
or quantify over holes. For instance, the phrase ‘There is a hole
in…’ can be treated as a mere grammatical variant of the shape
predicate ‘… is holed’, or of the predicate ‘...
has a hole-surrounding part’. (Challenge: Can a language be
envisaged that contains all the necessary predicates? Can every
hole-referring noun-phrase be de-nominalized? Compare: ‘The hole
in the tooth was smaller than the dentist's finest probe’, Geach
1968: 12.)

One may hold that holes do exist, but they are nothing over and
above the regions of spacetime at which they are found (Wake et
al. 2007). They are not just regions of space, for holes can
move, as happens any time you move a donut, whereas regions of space
cannot. But as regions of spacetime, they can be said to move in
virtue of having different temporal parts follow one another in
different places. (Challenge: Take the doughnut and spin it
clockwise. Take a wedding ring, put it inside the hole in the
doughnut, and spin it the other way. Both holes are spinning, though
in opposite directions, but the relevant temporal part of the little
hole is a spatiotemporal part of the big hole. Would it be spinning
in both directions?)

One may hold instead that holes are qualified portions of
spacetime (Miller 2007). There would be nothing peculiar about such
portions as opposed to any others that we would not normally think of
as being occupied by ordinary material objects, just as there would be
nothing more problematic, in principle, in determining under what
conditions a certain portion counts as a hole than there is in
determining under what conditions it counts as a dog, a statue, or
whatnot. (Challenge: What if there were truly unqualified portions of
spacetime, in this or some other possible world? Would there be truly
immaterial entities inhabiting such portions, and would holes be among
them?)

One might also hold that holes are ordinary material
beings: they are neither more nor less than superficial parts of what,
on the naive view, are their material hosts (Lewis & Lewis
1970). For every hole there is a hole-surround; for every
hole-surround there is a hole. On this conception, the
hole-surround is the hole. (Challenge: This calls for an
account of the altered meaning of certain predicates or
prepositions. Would a point on a hole-surround count as
being inside the hole? Would expanding the hole-surround
amount to enlarging the hole?)

Alternatively, one may hold that holes are
“negative” parts of their material hosts (Hoffman &
Richards 1985). On this account, a donut would be a sort of hybrid
mereological aggregate—the mereological sum of a positive pie
together with the negative bit in the middle. (Again, this calls for
an account of the altered meaning of certain modes of speech. For
instance, making a hole would amount to adding a part, and changing an
object to get rid of a hole would mean to remove a part, contrary to
ordinary usage.)

Yet another possibility is to treat holes as
“disturbances” of some sort (Karmo 1977). On this view, a
hole is to be found in some object (its “medium”)
in the same sense in which a knot may be found in a rope or a wrinkle
in a carpet. (The metaphysical status of such entities, however, calls
for refinements. Simons 1987: 308 has suggested construing them as
Husserlian moments that continuously change their fundaments, but this
seems to suit knots and wrinkles better than holes.)

Finally, it may be held that holes are not the particulars they
seem to be. Perhaps they are properties, or relations, which is to say
way things are (Meadows 2013). Or perhaps they are genuine absences,
understood as localized states of the world and, therefore, though not
things or natural properties or relations of things, they can serve as
truth-makers for negative existentials or false-makers for positive
existentials (Martin 1996).

On the other hand, the possibility remains of taking holes at face
value. Any such undertaking would have to account, not only for the general
features mentioned in section 1, but also for a
number of additional peculiarities (Casati & Varzi 1994). Among
others:

Holes are ontologically parasitic: they are always in
something else and cannot exist in isolation. (‘There is no such
thing as a hole by itself’, Tucholsky 1930.)

Holes are fillable. (You don't necessarily destroy a hole by filling it up. You
don't create a new hole by removing the filling.)

Holes are mereologically structured. (They have parts and can bear
part-whole relations to one another, though not to their hosts.)

Holes are puzzling creatures. The question of whether they are to be
subjected to Ockham's razor, reduced to other entities, or taken at
face value is an instance of the general question that philosophers
have to address when they scrutinize the ontology inherent in the
common-sense picture of the world.